This week the New York Federal Reserve Bank announced that its president, Bill Dudley, will retire next year. He will leave a mixed legacy. He is thought to have given important help to Janet Yellen, the outgoing chair of the Federal Reserve. But he also presided over a steep decline in his institution’s influence over the banks that used to revere and fear it.

Located in America’s financial centre, the New York Fed has powers not vested in the country’s 11 other reserve banks. Its president has a permanent seat on the Fed committee that sets interest rates. Its trading desk puts board policies into...